Variational Analysis of Metric Projections onto Isotone Projection Cones via Coderivatives

Abstract

In this paper, we study variational properties of the metric projection mapping onto isotone projection cones in finite-dimensional Euclidean spaces. We derive explicit formulas for both the Fréchet coderivative and the Mordukhovich coderivative of the projection operator. The analysis is based on a local description of the projection mapping via an associated generating system in a neighborhood of a reference point, which leads to computable coderivative characterizations. As an application, we compute the covering constant of the projection mapping, providing a quantitative description of its local regularity. Furthermore, we establish verifiable sufficient conditions for the Aubin property of the solution mapping associated with parametric nonlinear complementarity problems associated with isotone projection cones. The obtained results contribute to the variational analysis of metric projections in a general cone setting where orthogonality arguments are not available, and to the stability theory of complementarity systems in finite dimensions.